Non-vanishing at m -> 0 of the 1-loop self-mass of an electron of mass m propagating in a graphene-like medium in a constant external magnetic field

Bruno Machet (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

The 1-loop self-energy of a Dirac electron of mass m propagating in a thin medium simulating graphene in an external magnetic field B is investigated in Quantum Field Theory. Equivalence is shown with the so-called reduced QED_{3+1} on a 2-brane. Schwinger-like methods are used to calculate the self-mass \delta m_{LLL} of the electron when it lies in the lowest Landau level. Unlike in standard QED_{3+1}, it does not vanish at the limit m -> 0 ; \delta m_{LLL} -> (\alpha/2)\sqrt{\pi/2}\sqrt{\hbar |e|B/c^2},(with \alpha=e^2/4\pi\hbar c); all Landau levels of the virtual electron are taken into account and on mass-shell renormalization conditions are implemented. Restricting to the sole lowest Landau level of the virtual electron is explicitly shown to be inadequate. Resummations at higher orders lie beyond the scope of this work.

Mots clés: Quantum Electrodynamics in external magnetic field; electron self-mass; graphene

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]

Bruno Machet. Non-vanishing at m -> 0 of the 1-loop self-mass of an electron of mass m propagating in a graphene-like medium in a constant external magnetic field. 2016. ⟨hal-01346026⟩